"Trend, Seasonality and Economic Time Series:the Nonstationary Errors-in-variables Models"

Kunitomo, Naoto and Seisho Sato

June 2015

The use of seasonally adjusted (official) data may have statistical problem because it is a common practice to use X-12-ARIMA in the official seasonal adjustment, which adopts the univariate ARIMA time series modeling with some renements. Instead of using the seasonally adjusted data, for estimating the structural parameters and relationships among non-stationary economic time series with seasonality and noise, we propose a new method called the Separating Information Maximum Likelihood (SIML) estimation. We show that the SIML estimation can identify the nonstationary trend, the seasonality and the noise components, which have been observed in many macro-economic time series, and recover the structural parameters and relationships among the non-stationary trends with seasonality. The SIML estimation is consistent and it has the asymptotic normality when the sample size is large. Based on simulations, we nd that the SIML estimator has reasonable nite sample properties and thus it would be useful for practice.